Problem: Chubby Yang is studying linear equations right now. He came up with a nice problem. In the problem you are given an n × n matrix W, consisting of integers, and you should find two n × n matrices A and B, all the following conditions must hold: 

  * Aij = Aji, for all i, j (1 ≤ i, j ≤ n); 
  * Bij = - Bji, for all i, j (1 ≤ i, j ≤ n); 
  * Wij = Aij + Bij, for all i, j (1 ≤ i, j ≤ n). 



Can you solve the problem?

Input

The first line contains an integer n (1 ≤ n ≤ 170). Each of the following n lines contains n integers. The j-th integer in the i-th line is Wij (0 ≤ |Wij| < 1717).

Output

The first n lines must contain matrix A. The next n lines must contain matrix B. Print the matrices in the format equal to format of matrix W in input. It is guaranteed that the answer exists. If there are multiple answers, you are allowed to print any of them.

The answer will be considered correct if the absolute or relative error doesn't exceed 10 - 4.

Examples

Input

2
1 4
3 2


Output

1.00000000 3.50000000
3.50000000 2.00000000
0.00000000 0.50000000
-0.50000000 0.00000000


Input

3
1 2 3
4 5 6
7 8 9


Output

1.00000000 3.00000000 5.00000000
3.00000000 5.00000000 7.00000000
5.00000000 7.00000000 9.00000000
0.00000000 -1.00000000 -2.00000000
1.00000000 0.00000000 -1.00000000
2.00000000 1.00000000 0.00000000

Solution (in JAVA):

Solution:
//package com.security.lessons;

import java.io.BufferedOutputStream;
import java.io.PrintWriter;
import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
        solveB(scanner, out);

        out.close();
    }

    public static void solveA(Scanner scanner, PrintWriter out){
        String inputWord = "nineteen";
        String str = scanner.nextLine();
        Map<Character, Integer[]> repetition = new HashMap<>();
        Integer[] countLetter;
        //записываем количество попаданий буквы в слове nineteen
        for (int i = 0; i < inputWord.length(); i++) {
            if (!repetition.containsKey(inputWord.charAt(i))){
                repetition.put(inputWord.charAt(i), new Integer[]{1, 0});
            }else {
                countLetter = repetition.get(inputWord.charAt(i));
                countLetter[0]++;
            }
        }

        //считаем количество каждой буквы nineteen в строке
        for (int i = 0; i < str.length(); i++) {
            if (repetition.containsKey(str.charAt(i))){
                countLetter = repetition.get(str.charAt(i));
                countLetter[1]++;
            }
        }

        //находим минимальное число попадний буквы в строке
        int minimum = repetition.get(inputWord.charAt(0))[1];
        for (Map.Entry<Character, Integer[]> letter : repetition.entrySet()) {
            int min = (letter.getValue()[1]/letter.getValue()[0]);
            if (min == 0){
                out.println(0);
                out.close();
                return;
            }
            if (min < minimum && letter.getKey() != 'n'){
                minimum = letter.getValue()[1]/letter.getValue()[0];
            }
        }
        //особые условие для n


        int tmp = repetition.get('n')[1]/repetition.get('n')[0];
        int minN = (repetition.get('n')[1] - repetition.get('n')[0])/2 + 1;
        //show map. ВСЁ ОК. ДАЛЬШЕ ДВИГАЕМСЯ
        /*for (Map.Entry<Character, Integer[]> letter : repetition.entrySet()) {
            System.out.println(letter.getKey() + " in word = " + letter.getValue()[0] + ", " + letter.getValue()[1] + ",  " +
                    letter.getValue()[1]/letter.getValue()[0]);
        }*/

        if (minimum < minN){
            out.println(minimum);
        }else {
            out.println(minN);
        }
        //out.println(minimum);
        out.close();
        //eihstiirnmteejeehimttrijittjsntjejmessstsemmtristjrhenithrrsssihnthheehhrnmimssjmejjreimjiemrmiis
    }

    public static void solveB(Scanner scanner, PrintWriter out){
        int n = Integer.parseInt(scanner.nextLine());
        double[][] W = new double[n][n];
        double[][] A = new double[n][n];
        double[][] B = new double[n][n];

        for (int i = 0; i < n; i++) {
            String[] tmp = scanner.nextLine().split(" ");
            for (int j = 0; j < n; j++) {
                W[i][j] = Integer.parseInt(tmp[j]);
            }
        }
        // показ считанной матрицы
        //showMatrix(W, n, out);

        //поставить элементы матриц по главной диагонале

        //считать элементы матриц, которые внутри
        int iteration = n*n - n;
        double x, y;
        int count = 0;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                if (i == j){
                    A[i][j] = W[i][j];
                    B[i][j] = 0;
                }else{
                    y = (W[i][j] - W[j][i])/2;
                    x = W[i][j] - y;

                    A[i][j] = x; A[j][i] = x;
                    B[i][j] = y; B[j][i] = -y;
                }
            }
            if (count == iteration){
                break;
            }
        }

        showMatrix(A, n, out);
        showMatrix(B, n, out);

    }
    private static void showMatrix(double[][] W, int n, PrintWriter out){
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                out.print(W[i][j] + " ");
            }
            out.println();
        }
    }
}